This is from Uncanny X-Men #145-147, by Chris Claremont and Dave Cockrum.

Xavier recruits Polaris, Banshee, Havok, and Iceman to rescue the hostages, while the other X-Men go to get Arcade from Doom.

While Storm's with Doom, the other X-Men sneak in and try finding Arcade. However, Arcade's cell is empty, and they are attacked by some of Doom's armored-guards.

The X-Men defeat Doom's guards, and...

The other X-Men are placed in traps inside the castle. Meanwhile, Polaris, Banshee, Havok, and Iceman successfully rescue the hostages.

The X-Men start to escape from Doom's traps.

John Byrne would later have Doom claim that the Doom in this arc was a Doombot (in Fantastic Four #258).

However, since Doom destroyed the Doombot as part of a lesson he was teaching Kristoff (as opposed to being by himself), it's possible he was just lying about it.

Doom and Storm's relationship was later brought up in Steven A. Roman's Chaos Engine trilogy. In Book I, Doom uses the Cosmic Cube to change reality and take over the world. In the new reality, Storm is his wife.

Here's an illustration from the novel, by Mark Buckingham.

Here's the scene where the X-Men discussed Storm's relationship with Doom, after finding out they were married in the new reality.

"Yeah an' that's somethin' else I don't understand," Rogue said. "How is it that Ororo'd be willin' to marry that tin-plated nut, let alone agree to go rulin' the world with 'im? I don't see the connection between 'em."
"Before yer time, darlin'," Wolverine replied. "First run-in the new team had with Doom, he invited her t'dinner at his castle upstate while the rest o' us were dukin' it out with his goons in the basement. Some foolish attempt t'rescue that grinning jackass Arcade--the reasons why are too complicated t'get into right now. Least we thought it was a rescue mission; shoulda known better. Turned out to be a flamin' trap he set up for us with ol' metalhead."
Phoenix nodded. "Ororo confided in me about that once. She was... embarrassed by how she'd allowed herself to be drawn to Doom's power and... well, charisma. I guess, in the middle of a mission. And although he tried to kill her and our friends, she and Doom parted on civil terms--he even..." Jean paused, then shrugged. "Well, from the way Ororo described it, it sounded like Doom was hitting on her.""Hittin' on her?" Rogue asked incredulously. "This is Doctor Doom y'all are talkin' 'bout, right?"
"Well, that's what it sounded like when Ororo told me," Jean replied. "He said he found her 'fascinating,' and wanted to get to know her better. And Ororo--for some reason--was actually open to the idea, though she never took him up on the offer."
"Jus' like a woman, eh?" Gambit quipped. "Say she gon' call de next day, den never does."
The icy stares directed his way by Jean, Rogue, and Carol did wonders for wiping the smile off his face.